Jan 18 (Reuters) - Goldman Sachs Group Inc (GS.N) reported a fall in fourth-quarter profit on Tuesday due to weak trading activity, but a bumper year for mergers and acquisitions helped Wall Street"s premier investment bank post record full-year profits. Net earnings applicable to common shareholders fell to $3.81 billion in the quarter ended Dec. 31, from $4.36 billion the same period a year earlier. Earnings per share fell to $10.81 from $12.08 a year earlier. Analysts on average had expected a profit of $11.76 per share, according to Refinitiv data.